My Maths Thread

[nhmn0301]

Hi there,
Can someone show me how to do this question?

Calculate the area bound by the graph of y= 1 - (1/2)^(-x) , x=-2 and the x-axis. Give your answer in the exact form. (This is a Tech-free question)

Thanks!

[kinslayer]

Hi there,
Can someone show me how to do this question?

Calculate the area bound by the graph of y= 1 - (1/2)^(-x) , x=-2 and the x-axis. Give your answer in the exact form. (This is a Tech-free question)

Thanks!

First note that . It crosses the x-axis where x = 0 and it's a decreasing function for all x (looks like 1 - e^x). Therefore:

[nhmn0301]

Find the equation of a graph which will form a sphere of radius 3 units when rotated about the y-axis. Use volumes of revolutions to calculate the volume of this sphere.

Thank you!

[Zealous]

Find the equation of a graph which will form a sphere of radius 3 units when rotated about the y-axis. Use volumes of revolutions to calculate the volume of this sphere.

Thank you!

If you're a little confused at the working, a quick sketch of the graph might help you out!

If you use the standard formula you will get the same result. You can also derive the formula for the volume of a sphere using integration.